Cycling Hull with Slow-Relative-Motion Hydrodynamics

ABSTRACT

Device ( 1 ) creates slow-relative-motion hydrodynamics in a cycling hull ( 10 ) when multiplicity of hull sections ( 11 ) moves between multiplicity of rotatable end waterline turnabouts ( 20 ) and multiplicity of rotatable keel turnabouts ( 30 ). When device ( 1 ) moves across water, multiplicity of hull sections ( 11 ) cycles via connection to pivotable connection ( 12 ), which pivots about multiplicity of rotatable end waterline turnabouts ( 20 ) and multiplicity of rotatable keel turnabouts ( 30 ). This puts cycling hull ( 10 ) in motion. Since the bottom of multiplicity of rotatable keel turnabouts ( 30 ) is lower than the bottom of multiplicity of rotatable end waterline turnabouts ( 20 ), the portion of cycling hull ( 10 ) moving between multiplicity of rotatable end waterline turnabouts ( 20 ) and multiplicity of rotatable keel turnabouts ( 30 ) also travels the full draft of device ( 1 ). As there is no relative motion between the water and multiplicity of hull sections ( 11 ) as it cycles along the keel line set up between first keel turnabout with axle ( 31 ) and second keel turnabout with axle ( 32 ), so there is slow relative motion between the water and multiplicity of hull sections ( 11 ) as they cycle between multiplicity of rotatable end waterline turnabouts ( 20 ) and multiplicity of rotatable keel turnabouts ( 30 ). The slow relative motion can be quantified as the product of dividing the vertical distance between the waterline and the keel line by the horizontal distance between rotatable end waterline turnabouts ( 20 ) and rotatable keel turnabouts ( 30 ), which produces a percentage of the overall speed of device  1  as it moves across water.

CROSS REFERENCE TO RELATED APPLICATIONS

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FEDERALLY SPONSORED RESEARCH

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SEQUENCE LISTING OR PROGRAM

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BACKGROUND

1. Field

This invention pertains to boat hull design by facilitating aslow-relative-motion area between end turnabouts and keel turnabouts ina cycling hull.

2. Prior Art

The idea of eliminating relative motion at the water interface betweenthe turnabouts of a cycling hull has been recognized as possible sinceGeorge H. Young's patent for an “Improved Marine Car,” U.S. Pat. No.000,056,660, was issued on Jul. 24, 1866. While the aim of Young'sinvention was to reduce skin friction by eliminating relative motion,“residual resistance” (wave and turbulent resistance consideredtogether) is typically a bigger source of watercraft resistance than iswater friction, since residual resistance increases exponentially withincreases in watercraft speed. Thus, the churning of the water at theend turnabouts of a cycling hull, where the hull sections are plantedand pulled, presents a crucial challenge.

The strategy described herein to slow relative motion as cycling hullsections are planted and pulled next to the end turnabouts is found inno prior art. As a result, the potential of a cycling hull to createunprecedented efficiencies for marine transportation has goneunsuspected and unrealized.

An understanding of the objects and advantages of a cycling hull withslow-relative-motion hydrodynamics begins with an understanding of theidea that inspired the best prior art: wheeled efficiency is relevant towatercraft.

As the contact point of a rolling wheel is motionless relative to thesurface over which it moves, so the point of frictionless contactbetween a rolling wheel and its point on a solid can be extendedindefinitely by aligning a pair of wheels in a plane and using them asturnarounds for a continuous cycling track, as is commonly done with“caterpillar track.” There are two ways to apply this extendedno-relative-motion contact area between the turnabouts of a cyclingtrack to watercraft. Accordingly, there are two main branches in theprior art: (1) the cycling hull, in which the track itself is madebuoyant, and (2) a strategy to cycle the track around (or sometimespartially within) another source of buoyancy. In both cases a waterconveyance is created in which the percentage of the vessel that is inrelative motion against the water can be reduced indefinitely byextending the track. So, in both cases, the reason for the wheel'sextraordinary efficiency as a land conveyance is applied to waterconveyance to affect a near total reduction in water friction.

That said, the prior art affects an ironic squandering of efficiencythrough poor design choices. The squandering begins with Young whocalled the cycling hull that conveys his 1866 “Marine Car” a “ChainPropeller” in the drawing sheets, a designation which suggests afundamental misunderstanding of the true novelty of his invention:Whereas a watercraft propeller must engage water effectively, a waterconveyance achieves efficiency by reducing that engagement. In fact,Young's perspective was confused with respect to his invention's mainobjective, and an ironic approach to achieving marine efficiency usingcycling hulls that is endemic in the relevant art begins with Young.

Several design ironies with respect to efficiency are universal in thefirst or “cycling hull” branch of the prior art, but a transversecontouring of the hull sections is especially damaging. A transverseorientation sets up multiple instances of bluff form aerodynamicresistance as the cycling hull cycles. But if care is not taken to“streamline” the overall contour of the hull sections, increasing airresistance may outstrip the decrease in water skin friction. No care tostreamline the overall contour is taken in any of the cycling hullbranch of the prior art. That's curious, as the tradeoff for eliminatingrelative motion between the turnarounds is a doubling of air speedbetween the turnarounds when the hull sections are out of the water. Nowif the primary goal were to engage the water for propulsion, perhaps theunfortunate tradeoff from an efficiency standpoint would be worthwhile.But since the primary goal is more efficient conveyance through water, adesign uninformed by the need to minimize aerodynamic drag is clearlycounterproductive.

Because it ought to be obvious to anyone competent in the relevant artsthat aerodynamic efficiency should not be ignored with a cycling hullboat, the obvious advancement over the prior art attained bystreamlining the overall contour of the cycling hull sections is notclaimed herein. Nevertheless, is it important to note that 149 years ofprior art that is ironic with respect to efficiency provides no relevantcommentary on the potential of a cycling hull to improve the efficiencyof marine conveyance; and that, therefore, for all practical purposes,the art described herein constitutes the beginning of a productiveapproach to the design of an efficient cycling hull.

Specific examples of cycling hulls in the prior art begin, again, withU.S. Pat. No. 000,056,660 to Young (1866), and include U.S. Pat. No.424,076 to Pond (1890), U.S. Pat. No. 317,0533 to Fewel (1965), U.S.Pat. No. 4,715,668 to Burmeister (1987), and U.S. Pat. No. 6,582,258 toMorin (2003). Tellingly, only the earliest patents (to Young in 1866 andPond in 1897) have increased efficiency as an object. In the abstract itis surprising that no prior art, from this line of development, makes asophisticated attempt to realize the theoretical advantage that cyclinghulls have from an efficiency standpoint. In historical context it isclear that the rise of the internal combustion engine in the 20^(th)Century eclipsed market incentives to create disruptive technologicalefficiencies in the transportation industry.

A second universal flaw in the prior art, however, provides a moretelling reason for the primitive state of the prior art: The prior artdoes not address the main class of resistance to a vessel's movementthrough water (residual resistance). Thus, sophisticated designers canbe presumed to have surmised that cycling hulls are not worth thetrouble. We will return to this point after considering the other mainline of development originating with Young. But since the entire firstbranch prior art is ironic with respect to efficiency, it is pointlessto consider it further.

The other main branch of development subsequent to Young uses adisplacement hull in conjunction with a track which cycles eitherpartially inside the hull/hulls or around it/them. In these designs thetrack is either not buoyant or does not provide full buoyancy to thevessel—as the hull or hulls provide some or all of the buoyancy. In onesense the prior art that expounds this second course of development isnot relevant to the present invention (a cycling hull), since theprimary source of buoyancy does not cycle. But as a line of developmentwhich attempts to reduce resistance to the progress of a hull throughwater by using a cycling track it does represent a descendent of theinsight that inspired Young's 1866 innovation. (As used herein, unlike a“cycling hull,” a “cycling track” does not provide full designdisplacement by itself.)

Again, the effect of eliminating relative motion between the hullsurface and the water is to eliminate just “skin friction.” The hullssections must still push water aside in the manner of a traditionalwatercraft, thereby creating waves. And as the speed of the hull/waterinterface rises, movement at the boundary layer of water (where skinfriction occurs) gains kinetic energy, which spreads out from theboundary layer, creating turbulence. And again, since wave and turbulentresistance are usually classed together as residual resistance, sinceboth rise exponentially with the speed of the hull/water interface,residual resistance is typically the biggest source of resistance to themotion of a hull through water. So, if increasing watercraft efficiencyis the goal, an approach which neglects residual resistance constitutesa mostly ineffective strategy.

The entire second course of development since Young neglects residualresistance. Examples include U.S. Pat. No. 532,220 to Thomas (1895),U.S. Pat. No. 1,913,605 to Martin (1933), U.S. Pat. No. 2,091,958 toBraga (1937), U.S. Pat. No. 2,279,827 to Lapidovsky (1942), U.S. Pat.No. 2,377,143 to Golden (1945), U.S. Pat. No. 3,205,852 to Shepard(1965), U.S. Pat. No. 3,621,803 to Foster (1971), U.S. Pat. No.3,976,025 to Russell (1976), U.S. Pat. No. 4433634 to Coast (1984), U.S.Pat. No. 4,846,091 to Ives (1989), U.S. Pat. No. 5,845,593 toBirkestrand (1998), U.S. Pat. No. 5,845,595 to Atkinson (1998), and U.S.Pat. No. 6,482,053 to Prestenbach (2002). So there is no example of amostly effective strategy to address hydrodynamic resistance, as bothbranches of innovation fail to address residual resistance.

A single apparent exception to the wholesale dismissal of the prior forhaving no strategy to address residual resistance occurs in U.S. Pat.No. 6,508,188 to Jim Dong (Jan. 21, 2003), where Dong expresses themisunderstanding first evidenced in Young (with his designation of hisinvention as a “chain propeller” in his drawing sheets) as follows: “theuse of the belt [or track] for propulsion purposes is entirely contraryto the intended purpose of lessening the friction between the hull of avessel and the body of water through which it is passing.”

But Dong's underlying rationale is flawed, which made it seem that hiscreation of a very sophisticated innovation to reduce residualresistance was needed. First, he uses the underlying designpriority—clearly and truly expressed—to misunderstand a dual realitycrucial to grasping the design challenge at hand. The dual underlyingreality is that boats need propulsion and that the most efficientpropulsion occurs when the interface between the water and thepropulsion is as large as possible (less turbulence is created for anygiven power input when that input is spread over a larger interface).But the largest possible interface between a watercraft and the waterthrough which it moves is the full displacement affected by thewatercraft. So, yes, Dong's point is well taken that it is the“lessening of the friction between the hull of a vessel and the waterthrough which it is passing” which expresses the primary goal; but thatdoes not eliminate the fact that the vessel's full displacement presentsthe best possible opportunity to create efficient propulsion, and thatthe full displacement should often be used for propulsion in conjunctionwith a cycling hull or track, as a cycling hull uniquely makes thatpossible. (Exceptions would only occur where (1) it is desirable to towa cycling hull, or (2) when the motive force of hydrodynamic resistanceputting the cycling hull in motion will be smaller than the resultingaerodynamic resistance. The second case can arise when the cycling hulldesigner targets the sweet spot between 4 knots where water resistancetypically spikes and 14 knots where air resistance does so.) In short,not only are propulsion and conveyance not intrinsically at odds, oftena convergence of the two will be desirable for achieving maximumefficiency in a marine vessel.

And second, Dong invented a complex solution—submarine hulls envelopedwith cycling exteriors set on struts to support the topside of awatercraft—to address residual resistance. The need for a complexsolution derives both from Dong's false grasp of the underlying reality(seeing propulsion as necessarily pitted against conveyance), and fromoverlooking a design feature of all efficient watercraft which can beincorporated into the design of a cycling hull (explained below).Accordingly, his patent is not an exception to the wholesale dismissalof the prior art as a set of ironic designs. So we turn to the presentinvention, which redresses the main failure of the prior art: the needfor a design of a cycling hull that targets residual resistance.

The design feature incorporated into all traditional watercraft whenreducing residual resistance is the primary goal is a finely graded bowand stern. (Only seeming exceptions result when design considerationsother than efficiency are given priority, including when sufficientpower is applied to a planing boat or a hydrofoil to ignore theinefficiency of bringing the watercraft into a planing or lift-off modeand keeping it there.) This design feature can be incorporated into acycling hull as simply as it is incorporated into traditionaldisplacement watercraft: As traditional watercraft effect a fine angleof entry and exit for a displacement hull as it moves through the water,so a cycling hull can set up a fine gradient of entry and exit for thehull sections as they are planted into and pulled from the water.

From one standpoint the analogy is exact: in both cases the hydrodynamicinteraction that creates wave resistance—one of the two main factors inresidual resistance—is reduced by slowing the speed at which the hullparts and pulls away from the water. From another it is not: the actualspeed at which the hull moves relative to the water clearly is notslowed by setting up fine bow and/or stern angles, whereas setting upfine gradients of entry/exit for cycling hull sections does slow therelative speed of the hydrodynamic interaction. In fact, the slowing canbe large, 90% and more. For example, setting up the same angle forcycling hull sections as they are planted and pulled as an efficientkayak uses as its angles of entry and exit at its bow and stern producesa 90% reduction in hull speed. (An 18 foot long hull with a 20 inch beamis typical, and will part the water at 7.5% of the speed at which thekayak moves through the water. In the case of a cycling hull that setsup the same angle to plant and pull the hull sections, 92.5% of therelative speed of the hull sections will be eliminated.)

Let's take stock of how a cycling hull with a slow-relative-motion areabetween the end turnabouts and the point where the hull sections reachfull draft compares to both a cycling hull without thisslow-relative-motion area and to a traditional watercraft.

First consider a cycling hull without a slow-relative-motion area nextto the turnabouts. It will virtually eliminate water friction over mostof its “wetted surface,” but has little ability to address wave makingand turbulence at the turnabouts. Second consider a traditionalwatercraft. It can set up a fine angle of entry to reduce waveresistance, but it has limited ability to address water friction andturbulent resistance. But the case of a cycling hull with aslow-relative-motion area next to the turnabouts is different. It will(1) virtually eliminate water friction over most of its wetted surface;it can (2) eliminate most of the wave resistance—where designed to doso, by more than 90%—by slowing the hydrodynamic interface, which will(3) also eliminate most of the turbulent resistance. So a cycling hullwith slow-relative-motion next to the end turnabouts addresses all threemajor forms of hydrodynamic resistance, whereas traditional watercraftand the cycling hull without the slow-relative-motion area are bothmostly effective with only one of the three major factors. Furthermore,since wave and turbulent resistance increase exponentially withincremental increases in watercraft speed, the addition of aslow-relative-motion area will theoretically make much more than a 90%reduction in those forms of resistance, given a realistic 90% reductionin the ratio of the speed of hydrodynamic interaction to overallwatercraft speed, in many cases.

An unprecedented decrease in hydrodynamic resistance, then, can beproduced by combining an insight taken from traditional watercraft andcombining it with an insight taken from the work—basically unaltered forthe better with respect to efficiency over 149 years—of George Young in1866.

In short, the principle that wheels utilize to (theoretically) eliminatefriction is combined with the principle by which a fine angle of entry(and usually exit) used in good traditional displacement hulls reduceswave-related resistance, and that combination creates a synergisticefficiency that affects reduced hydrodynamic turbulence as well. So acycling hull with slow-relative-motion hydrodynamics possesses a uniqueability to dramatically reduce all major forms of hydrodynamicresistance without either (1) requiring large initial and sustainingpower inputs in the cases of planing hulls and hydrofoils, or (2)resorting to submarine hulls with cycling exteriors.

While all cycling hulls have turnabouts at the ends, the presentinvention uniquely places turnabouts to set up full-draft placement ofthe cycling hull as it moves along the keel. That placement makes itpossible to form a fine gradient for the cycling hull sections as theyare planted into and pulled out of the water. It is the use of theturnabouts to create a fine gradient, which thereby affect aslow-relative-motion interface with the water for the hull sections asthey are planted and pulled, which will be claimed.

SUMMARY

The prior art does not set up a finely graded entry into and exit fromthe water for the cycling hull sections, which is analogous to the fineentries at the bow and stern of efficient displacement watercraft hulls.It is by means of this finely graded entry and exit for the hullsections that a cycling hull produces slow-relative-motionhydrodynamics. By setting up slow-relative-motion areas a cycling hullwith slow-relative-motion hydrodynamics can reduce almost all of thethree major sources of hydrodynamic resistance (skin friction,turbulence, and waves), which no other form of water conveyance can dowithout either (1) applying relatively large power inputs to begin andsustain a high-speed hydrodynamic interface, as with planing watercraftand hydrofoils, or (2) relying on submarine hulls with cyclingexteriors. Because the present invention alone utilizes a familiar andrelatively simple technology (“caterpillar track”) to affect itssurprising hydrodynamic advantages, the present invention has a uniquepotential to increase watercraft efficiency.

DRAWINGS Figures

FIG. 1 is a perspective drawing of the present invention from a point ofview above and to one side. The waterline depicted therein is not partof the present invention, but is included in FIG. 1 to provide a contextfor how the present invention will be situated in the medium of itsintended use.

FIG. 2 is a perspective drawing of the near lower quarter of the presentinvention from a point of view above and to one side. FIG. 2 affords amore detailed view of the present invention's components. Beingsymmetrical in all directions, all of the present invention can beextrapolated from FIG. 2.

Reference Numerals

1 device

10 cycling hull

11 multiplicity of hull sections

12 pivotable connection

20 multiplicity of rotatable end waterline turnabouts

21 first end waterline turnabout with axle

22 second end waterline turnabout with axle

30 multiplicity of rotatable keel turnabouts

31 first keel turnabout with axle

32 second keel turnabout with axle

40 forked frame

DETAILED DESCRIPTION FIGS. 1-2—Preferred Embodiment

To understand this description fully, it should be read with FIG. 1 andFIG. 2 in view. In referring to this invention and the parts which itcomprises, the reference numerals provided above shall be usedthroughout the following description.

I begin with FIG. 1. There depicted is a perspective view of the presentinvention as seen from above, to the left of longitudinal center, andfrom a vantage point in the foreground. (Because the embodiment of thepresent invention depicted herein is symmetrical in all directions fromits center point, references to spatial orientations are projected fromthe observer's frame of reference. The exception is the verticaldimension, where the waterline establishes the bottom of the verticalorientation.) The preferred embodiment of device 1 comprises these majorcomponents: cycling hull 10, multiplicity of rotatable end waterlineturnabouts 20, multiplicity of rotatable keel turnabouts 30, and forkedframe 40. The bottom of first keel turnabout with axle 31 is lower thanthe bottom of first end waterline turnabout with axle 21. And the bottomof second keel turnabout with axle 32 is slightly lower than the bottomof second end waterline turnabout with axle 22. The waterline depictedis not part of the preferred embodiment, but is indicated to show howthe present invention is situated in the medium of its intended use.

FIG. 2 shows the left lower quarter section of the preferred embodimentfrom a perspective similar to FIG. 1. This view shows how multiplicityof hull sections 11 is connected to pivotable connection 12, and howpivotable connection 12 is situated to pivot about first end waterlineturnabout with axle 21 and first keel turnabout with axle 31, therebyallowing cycling hull 10 to cycle.

Because device 1 is symmetrical around its center point in alldirections, device 1, in its entirety, can be extrapolated from theperspective view of one quarter section provided in FIG. 2.

Operation—FIGS. 1 and 2

From the description above it is apparent that the present inventionemploys a strategy to cycle cycling hull 10 about first end waterlineturnabout with axle 21, first keel turnabout with axle 31, second keelturnabout with axle 31, and second end waterline turnabout with axle 32.It is apparent that where cycling hull 10 descends from the bottom offirst end waterline turnabout with axle 21 toward the bottom of firstkeel turnabout with axle 31 (assuming that device 1 moves in thedirection of first end waterline turnabout with axle 21) it forms a finedownward gradient. Simultaneously, where cycling hull 10 moves from thebottom of second keel turnabout with axle 32 toward second end waterlineturnabout with axle 22, it forms a fine upward gradient. The finegradients thereby set up between multiplicity of rotatable end waterlineturnabouts 20 and multiplicity of rotatable keel turnabouts 30 span thevertical distance between where cycling hull 10 first contacts water andwhere it reaches full draft under multiplicity of rotatable keelturnabouts 30. The fine gradients that cycling hull 10 thereby forms asit is planted into and pulled out of the water createsslow-relative-motion hydrodynamic interface as device 1 cycles acrosswater.

Advantages

By creating slow-relative-motion hydrodynamic interfaces where thecycling hull is planted into and pulled from the water, the presentinvention reduces wave and turbulent resistance, which is otherwiseunabated at the end turnarounds of a cycling hull. As a result, thepresent invention implements a strategy to reduce all three major formsof hydrodynamic resistance—skin friction, and wave and turbulentresistance. By comparison the relevant prior art (except that whichresorts to submarine hulls with struts to support topside structure)addresses only skin friction. Displacement hulls, on the other hand, canmake a mostly effective reduction in wave-making resistance only (bycreating a high aspect ratio craft with a fine bow and stern). Andplaning and hydrofoil hulls can reduce all three major forms ofhydrodynamic resistance, but only at the cost of relatively high initialand sustained power inputs (used to raise and sustain these forms ofwatercraft in planing or lift off mode). A mostly effective strategy toreduce the three major forms of hydrodynamic resistance withoutrequiring high initial and sustained power inputs or resorting to asubmarine hull with a cycling exterior, then, comes down to the presentinvention.

Conclusion, Ramifications, and Scope

The present invention embodies the one strategy that can reduce amajority of all three major forms of hydrodynamic resistance withouteither requiring high initial power inputs or resorting to a submarinehull with a cycling exterior supporting a top side mounted on struts. Itthereby creates a new category of efficient watercraft hull: cyclinghulls with slow-relative-motion hydrodynamics set up by situatingturnabouts so that they cycle hull sections at a fine angle between thepoints of first water contact and full draft placement along the keelline.

As no particular means of steering and propelling traditional boat hulls(paddles, oars, sails, skegs, rudders, outboard motors with propellers,inboard motors with propellers, etc.) is essential to the concept of atraditional boat hull, so none is essential to a cycling hull withslow-relative-motion hydrodynamics. Neither is the fact that a cyclinghull can uniquely use the hull itself as the means of propulsion—byadding a drive axle to one or more of the turnabouts—an essentialfeature of the present invention, as the efficiencies gained by addingslow-relative-motion areas to a cycling hull are gained whether or notan “active” or “passive” track is employed. Again, the essential anddefining feature of the present invention is the use of turnabouts, asdescribed herein, to set up slow-relative-motion areas where the cyclinghull sections are planted into and pulled out of the water when acycling hull moves across water. It is the placement of the turnaboutsso that they affect a fine gradient of entry and exit for the cyclinghull sections, analogous to the fine gradient used at the bow and(usually)the stern of good displacement hulls, then, that forms the essentialfeature of a cycling hull with slow-relative-motion hydrodynamics.

That essential feature can be used in parallel iterations of cyclinghulls with slow-relative-motion hydrodynamics, just as traditional hullsare aligned in parallel iterations to make catamarans, trimarans, and soforth. This is obvious.

What may not be immediately obvious is that a cycling hull can standalone—Literally—when operated and so form a usable watercraft when notused in conjunction with another cycling hull. But whether such use isobvious is moot, as the same dynamics which allow two-wheeledvehicles—bicycles and motorcycles—to operate without lateral supportwhile in use will be in play when a single cycling hull operates.Accordingly, there is nothing to invent, as the possibility of using acycling hull as a stand-alone hull has existed all along. (True, arudder to steer the cycling hull will be essential in the case ofoperating a single cycling hull, but that will be obvious to anyoneskilled in the relevant art, voiding any a claim to that novelty.)

So we are left with the essential feature of a cycling hull as definedin the claim to follow.

I claim:
 1. A cycling hull with slow-relative-motion hydrodynamics,comprising: (a) a multiplicity of rotatable end waterline turnaboutshaving a first end waterline turnabout with axle and a second endwaterline turnabout with axle, (b) a multiplicity of rotatable keelturnabouts having a first keel turnabout with axle and a second keelturnabout with axle, said multiplicity of rotatable keel turnaboutsbeing aligned horizontally with and inboard of said multiplicity ofrotatable waterline turnabouts in a substantially vertical orientationwith the bottom of said multiplicity of rotatable end waterlineturnabouts being situated higher than the bottom of said multiplicity ofrotatable keel turnabouts, (c) a forked frame for securing saidmultiplicity of rotatable end waterline turnabouts and said multiplicityof rotatable keel turnabouts, and (d) a cycling hull having amultiplicity of hull sections and a pivotable connection by means ofwhich said multiplicity of hull sections can cycle about saidmultiplicity of rotatable end waterline turnabouts and said multiplicityof rotatable keel turnabouts, whereby a cycling hull, while cyclingacross water, creates a gradual descent for its hull sections as theymove from first water contact toward full draft placement at the keelline and a gradual ascent for its hull sections as they move from fulldraft placement at the keel line toward last contact with the water.